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A subgrid-scale model for large-eddy simulation based on the physics of interscale energy transfer in turbulence

A SUBGRID-SCALE MODEL FOR LARGE-EDDY SIMULATION BASED ON
THE PHYSICS OF INTERSCALE ENERGY TRANSFER IN TURBULENCE
by
Brian Wayne Anderson
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(AEROSPACE ENGINEERING)
May 2012
Copyright 2012 Brian Wayne Anderson

In large-eddy simulation (LES) various subgrid-scale models have been proposed, all of which attempt to account for the unknown effects of the unresolved scales of turbulence on the resolved flow-field. The scale-similarity model is one such model, which is formulated using a secondary filter applied to components of the resolved velocity and its products. The scale-similarity model is based on the assumption that the velocities associated with neighboring scales in the flow produce turbulent stresses that are similar in character. The model uses an expression that weights the scales just below the LES cutoff in its approximation of the stresses of the unresolved scales. It is well-known, however, that the similarity model fails to accurately predict some of the most fundamental quantities in turbulent flows, perhaps the most important being the global energy transfer and the associated subgrid-scale dissipation. In previous research, additional dissipative terms have been added to the similarity model to improve the model's performance. ❧ In the present research, considerations of interscale energy transfer have been used to identify the deficiencies of the energy transfer role of the similarity model, specifically its inadequate removal of terms contributing energy to the smallest scales and its duplication of terms producing effects in the largest scales. These considerations are then used in the development of a new model, which shows more favorable characteristics of energy transfer. In this approach, partial nonlinear terms are used to decompose the nonlinear transfer present in LES and to formulate an expression capable of removing small-scale production terms depositing energy near the LES cutoff. The proposed model is formulated in the same vein as the scale-similarity model, consisting of test-filtered velocities and their products, but the new interscale transfer model offers improvements in its predictions of mean flow quantities and the global energy flux from the resolved to subgrid scales. The current research demonstrates that by implementing this model in a posteriori LES testing of wall-bounded flows, improved LES predictions are possible without the need for additional terms to augment subgrid-scale energy dissipation.

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A SUBGRID-SCALE MODEL FOR LARGE-EDDY SIMULATION BASED ON
THE PHYSICS OF INTERSCALE ENERGY TRANSFER IN TURBULENCE
by
Brian Wayne Anderson
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(AEROSPACE ENGINEERING)
May 2012
Copyright 2012 Brian Wayne Anderson